Calculate this probability

[plindboe]

If a person is asked 40 questions, each of them binary(yes or no type questions), then what is the probability of getting at least 35 of them correct?

Help much appreciated. :)

[CFLarsen]

Make your question one of the 40 questions. ;)

[geni]

assumming aswers are given at random then I think it is:

40C35 (0.5)³⁵(0.5)⁵

about 6*10<sup>-7</sup

[scribble]

Originally posted by plindboe
If a person is asked 40 questions, each of them binary(yes or no type questions), then what is the probability of getting at least 35 of them correct?

Help much appreciated. :)

It depends on the questions and the person answering, of course. If you asked me 40 yes/no questions on C++ programming, I'd be ashamed to not get a perfect 40, for example.

I don't think we can answer this.

[TeaBag420]

Originally posted by plindboe
If a person is asked 40 questions, each of them binary(yes or no type questions), then what is the probability of getting at least 35 of them correct?

Help much appreciated. :)

Unsolvable as stated. Is the person answering randomly? Does he know the answers to any of the questions? Does the questioner know what the person knows?

In the most stripped down possible version, the probability is a bit less than 12.5 %, the same as the probability of getting at least 35 questions wrong.

Remember when Steven Seagal was asked about Mt. Everest in the Glimmer Man?

[plindboe]

Originally posted by scribble
It depends on the questions and the person answering, of course. If you asked me 40 yes/no questions on C++ programming, I'd be ashamed to not get a perfect 40, for example.

I don't think we can answer this.

How silly of me, I should have specified. I'm talking about 50/50, like a coin toss.

I'm just having a discussion, with a proclaimed psychic, about the Larry King Live transcript below, and am interested in what the probability would be:

http://edition.cnn.com/TRANSCRIPTS/0106/05/lkl.00.html

KING: James, give us a simple example. What might be something you would ask her to do that could win her a million dollars? I know about writing it all up and everything. Give me an example. What -- you meet with her next week. You would say to her what?
RANDI: We would sit down and determine what she believes her powers are and to what extent they go, how far they will go, with what accuracy they will go. And then we would agree on a set of questions that would be asked that would have to have answers correct within a certain degree. We can do this.
KING: A question like -- like what? All right, give me an example.
RANDI: Such things as the gender of a person. That's a yes or no. That's a binary question, either right or wrong. Related, not related, old or young. And we'd have to determine what that would mean, too. A set of binary questions like this could easily decide whether or not Rosemary has the power.
KING: And how many questions would you want to have her respond to? As an example.
RANDI: It depends on what she says she can do and with what accuracy.
KING: With what you've seen tonight, what would you set up? How many questions?
RANDI: Oh, I would set up at least 40 questions.
KING: For -- and if she were right on 35, would she fail to get the million?
RANDI: You'd have to talk to a statistician about that, Larry. I'm not a statistician.
KING: Well, what would -- you give me an example.
(CROSSTALK)
What would you give the million for? What would you give the million for? Would she have to get 40 right?
ALTEA: Another wall.
RANDI: I can't talk the statistics with you. We have to refer that to our statisticians.
ALTEA: Another lock on the door. It's a very good trick, James, and I applaud you.
RANDI: There are no tricks being imposed here by me, Rosemary.
ALTEA: I think it's a really good trick. I think...
RANDI: The tricks are on your part.
ALTEA: Yeah, I think...
RANDI: I don't play tricks on people when I'm doing these tests.
ALTEA: Well...
RANDI: We agree at the test in advance, and you either pass or you don't pass. Will you try, yes or no?
KING: I'm asking a simple question, James. What is passing?
RANDI: It depends on what the test is, Larry. We have to assign the statistics to it.
KING: All right. A 40-question test, what passes? You know you're going to give away a million dollars.
RANDI: That's true.
KING: The statistician -- I assume you know statisticians. I assume you...
RANDI: No, I don't -- I know statisticians.
KING: You've never...
RANDI: I don't know statistics.
KING: So if she met with you tomorrow, you couldn't tell her what -- how many of the 40 she'd have to answer.
RANDI: Yes, I could, because I would have the right people on hand to advise me on the statistics. It's that simple.
KING: And if they told you she was 30 percent right, that would be considered extraordinarily accurate and you'd give her the million, if she had the 30 of the 40 questions right?
RANDI: If that were the statistical expectation that we could have, yes.
KING: Ah! But who sets the expectation? You can't tell us -- you have to give the statistician the expectation.
RANDI: That's right.
KING: The -- what do you ask him that he give you?
RANDI: The statistician will tell us what is significant in a set of binary questions, yes. The statistician will tell us if there were 40 questions, she would have to get x number right.
KING: I see.
RANDI: If there were 50 questions, you'd have to get...
ALTEA: I have something I don't understand.
KING: And he or -- and he or she, the statistician, would define "significant"?
RANDI: Yes, that's true.
ALTEA: I have something I don't understand. I have something here that I don't understand, because if -- James, what you're doing, and this deal is really genuine and you really expect to give it away this million dollars...
RANDI: No, I don't expect to give it away, no.
ALTEA: Well, OK -- well, you put it out there.
RANDI: I'm offering it to you.
ALTEA: OK, OK. If you -- well, then, you know, if you're seriously offering, not just to me but to anyone, I would have thought you'd really got this down. You would have had your numbers, you would have had your statisticians.
I mean, a million dollars is a lot of money. You don't just give it away and then come on TV show and say, well, it depends on this, it depends on...
RANDI: It all depends on what you claim your powers are and what your accuracy is.
ALTEA: I -- you know, I'd love you to you listen to this show. If you're recording this show, I would love you to listen to this show afterwards, because you're doing to me, to us, exactly what you're claiming I do to other people. You're doing exactly -- you are fishing, you are...

Would be great, if people could calculate the probability of 30/40 right answers as well.

[geni]

Originally posted by plindboe



Would be great, if people could calculate the probability of 30/40 right answers as well.

40C30 (0.5)³⁰(0.5)¹⁰

7.7*10^-4

It should be noted this this is the probability for exactly that number. To work out 30+ would be a different problem.

[JamesM]

The probability of getting at least 35 correct is 6.9e-7.
The probability of getting at least 30 correct is 1.1e-3 - that's about 0.1%.

[plindboe]

Originally posted by geni
40C30 (0.5)³⁰(0.5)¹⁰

7.7*10^-4

It should be noted this this is the probability for exactly that number. To work out 30+ would be a different problem.

Thanks for the help, but this seems like too low a probability to me. I mean, with a coin toss, getting 30 tails out of 40 coin tosses shouldn't be that hard, just random chance

I know most people don't have a good sense of statistics, myself included, but 30/40 just seems like nothing out of the ordinary to me.

What does 40C30 mean? What does the C stand for?

[JamesM]

Incidentally, if you're interested in the number you'd have to get right for a certain level of significance, here they are, for 40 trials:

5%: 23/40
1%: 27/40
0.1%: 30/40

What this means is, if you were to repeat the test many, many times, and the so-called medium really was just guessing, you'd expect to get a score of above 23/40 5% of the time, and so on.

As you can see, getting more than 30 right by dumb luck would be a fairly rare occurrence.

[geni]

Originally posted by plindboe
Thanks for the help, but this seems like too low a probability to me. I mean, with a coin toss, getting 30 tails out of 40 coin tosses shouldn't be that hard, just random chance

I know most people don't have a good sense of statistics, myself included, but 30/40 just seems like nothing out of the ordinary to me.

The probability for gettting 50/50 is about 1/4 so don't be suppised that the probability falls off fast


What does 40C30 mean? What does the C stand for?

It means that you press the buttion marked nCr on your calculator between the 40 and 30. It is to do with a horible bit of algerbra that I haven't looked at for about 3 years. The number being calculated there is the number of posible combinations in which those answers can be arranged (note combinations not permutations).

[JamesM]

Originally posted by plindboe
I know most people don't have a good sense of statistics, myself included, but 30/40 just seems like nothing out of the ordinary to me.

What we have here is a binomial probability problem: you have a series of n trials, with the outcome being a simple binary yes/no, the probability of success being p.

For the binomial distribution, the expected number of successes is np, and the variance is np*(1-p).

In this case, n = 40, and p = 0.5, so:

the expected number of successes = 40*0.5 = 20
which is what you'd expect intuitively.

The variance = (40*0.5)*(1-0.5) = 10.

The square root of the variance, the standard deviation, is in the same units as the observation (in this case, correct guesses), so let's use that instead:

the standard deviation = sqrt(10), about 3.2 correct guesses.

The standard deviation measures the "spread" of the observations from its expected value, so for this experiment we might expect to get 20 right, give or take 3.2.

As you can see, getting 30 right would be more than 3 standard deviations from the expected value, which is a fairly large deviation, hence it is rather unlikely, despite what you might think.

Hope I haven't messed any of the maths up.

[plindboe]

Thanks alot for the answers(especially geni and JamesM). :)

[T'ai Chi]

Originally posted by plindboe
If a person is asked 40 questions, each of them binary(yes or no type questions), then what is the probability of getting at least 35 of them correct?

Help much appreciated. :)

With n = 40, and p = .5, sum

nCr(n,r)*p^r*(1-p)^(n-r)

(where nCr = n!/[r!(n-r)!])

from r = 35 to r = 40

Doing that I get

.0000006913

[phildonnia]

Never mind. I type faster than I think.

[TeaBag420]

I especially like the part where Randi says he does and doesn't know statisticians. "Which is it?" is the question the Frog should have asked.

Also where he accepts the Frog's equation of 30/40 with 30%.

Perhaps a little too much Jesus Juice before the show.

[DevilsAdvocate]

Originally posted by TeaBag420
I especially like the part where Randi says he does and doesn't know statisticians. "Which is it?" is the question the Frog should have asked.

Also where he accepts the Frog's equation of 30/40 with 30%.

Perhaps a little too much Jesus Juice before the show.

Originally posted by plindboe
KING: The statistician -- I assume you know statisticians. I assume you...
RANDI: No, I don't -- I know statisticians.
KING: You've never...
RANDI: I don't know statistics.


I don;t always agree with the way Randi defends his positions, but I think in this case he was fairly clear.

Randi doesn't say he doesn't know statisticians. His answer "No, I don't" appears to be in response to King's question "I assume you..." which Randi may have been guessing would be something along the lines of "if you know statisticians, you must know something about statistics and can give me a number".

King was trying to get Randi to give a number, and Altea was accusing Randi of trickery because he wouldn't give an exact number. It appears at this point that Randi was getting a bit fed up with being pressed for a number that he couldn't provide and began anticipating King's line of questioning. To which he replied (in my interpretation "No, I don't know statistics -- I know statisticians who would help me with the statistics

It appears Randi clarifies the reply "No, I don't" when he immediately cuts off King again and says "I don't know statistics."

Also, Randi did not agree with King that 30 of 40 would be 30 percent. He didn't disagree either. Which is what would be expected if Randi doesn't know statistics.

[DevilsAdvocate]

Here are the probabilities of getting at least r number of right answers out of 40 questions where each question has a 50% chance of guessing right. This uses the following formula: (40!/(r!*40-r!)) * (.5^r) * (.5^(40-r)).

You may notice that it is actually MORE THAN LIKELY that you will get 20/40 questions correct. If this seems counterintuitive, consider if there are just 2 questions asked. You can get either 0, 1, or 2 right. The possible outcomes (r = right, w = wrong) are ww, wr, rw, rr. So there is a 75% chance of getting 1/2 quetsions right.

If you wanted to be over 1 in 1000 chance out of 40 questions, you would have to get at least 31 questions right. To be over 1 in 1 million would be 35 right (which by chance would be about .7 in 1 million).

The really hard part would be coming up with questions that actually have a 50% probability of being correct. For example, the ratio of males to females is not exactly 50% and can vary depending on the demographic group. So if either the psychic or the person choose the subject have any knowledge of the group from which the subject is chosen and the demographics of that group, then the test will be skewed. Therefore the questions must be agreed upon to have a 50% chance (or having a different weight of chance) and the person choosing the subject must be blind to the questions.

Here are the probabilties:

Right Chance
0 100.0000000000%
1 99.9999999999%
2 99.9999999963%
3 99.9999999253%
4 99.9999990267%
5 99.9999907149%
6 99.9999308694%
7 99.9995817708%
8 99.9978861489%
9 99.9908917085%
10 99.9660225873%
11 99.8889283113%
12 99.6786711952%
13 99.1705498313%
14 98.0761345858%
15 95.9654766124%
16 92.3070027919%
17 86.5906374473%
18 78.5204746078%
19 68.2085998686%
20 56.2685343810%
21 43.7314656190%
22 31.7914001314%
23 21.4795253922%
24 13.4093625527%
25 7.6929972081%
26 4.0345233876%
27 1.9238654142%
28 0.8294501687%
29 0.3213288048%
30 0.1110716887%
31 0.0339774127%
32 0.0091082915%
33 0.0021138511%
34 0.0004182292%
35 0.0000691306%
36 0.0000092851%
37 0.0000009733%
38 0.0000000747%
39 0.0000000037%
40 0.0000000001%

[TeaBag420]

I accept your corrections. I was wrong.

If Randi doesn't know statistics, how does he evaluate the qualifications of statisticians? Is there a certifying body with established standards? If he hires people to evaluate their qualifications, who evaluates THEIR qualifications?

Too much thought.... must get Jesus Juice.

[DevilsAdvocate]

Originally posted by TeaBag420
I accept your corrections. I was wrong.

If Randi doesn't know statistics, how does he evaluate the qualifications of statisticians? Is there a certifying body with established standards? If he hires people to evaluate their qualifications, who evaluates THEIR qualifications?

Too much thought.... must get Jesus Juice. That opens a differnt philosophical can of worms: how do you know what is true? Why do you believe what you believe? When do you accept a belief as true? Tough questions.

We have seen a number of different answers to the same question: some wrong, some right, some right but actually answer a different question. Statistics can be proven mathematically, but who knows if the math is correct?

You might say that Randi has (gulp) FAITH that his satisticians are correct. Actually, the staisticians' results can be verified by proven repeatable results. I'm sure that you can find statisticians that you can trust to be accurate -- it's not really that hard (and I'm not saying that you should trust my numbers -- I could be wrong).

Anyway, for the JREF challenge it doesn't matter much whether the statisticians are right or wrong as long as the protocol is agreed upon. If Randi's stats people say getting 21 out of 40 is acceptable and the psychic gets just a little lucky, then so be it. JREF loses 1 million$ but most people probably won't acept this as paranormal. The real problem would be if JREF's stats people set the bar impossibly high, which would be cause for believers to acuse JREF of being unfair.

In my opinion, I think the bar for "paranormal" should be set very high. There should be a clear distinction between "incredible chance", "amazing capability to deduce information (like the guy Sherlock Holmes as based on or certain cold readers) and truly "paranormal".

I can understand that a psychic's ability could exist that would be somewhat fuzzy, that would sometimes work and sometimes not, that would require the right concentration and conditions. I can spell and I can type, but my spelling and typing in this post probably aren't perfect. I can also understand that a psychic's ability may be determined on what they can "see".

For example, if I calimed to be abl to "see" certain things about a person (which happens to be because I have a fuzzy, grainy photo of them) I could tell you certain things about the person. But if I had a presceipted list of questions, the answers to those questions may not be available in the photo that I see. So I might fail the test miserably, but actually have the abilty to "see" certain things about the person. So is the test proposed by Randi really fair?

This is one reason why Randi and JREF have to make different protocols for each cliamaint, and why they are so difficult. In my opinion, to prove paranormal abilty, a psychic should be able to tell you a certain number of things about a person just as I would if I looked at a fuzzy, grainy photo of the person. If I told you some things about a person in a fuzzy, grainy photo then I might get some things wrong, but I should be WAY beyond probability. After all, I really can "see" them (in the bad photo). And I should be able to prove my ability to describe things about a person in a fuzzy, grainy photo WAY beyond probabilty with repeatable results. I think I can do this with lokking at poor photos. Can psychics do this by paranormal means? Not that I've seen.

[DevilsAdvocate]

I hope Randi has a bit more knowledge of statistics than what he let on in the King interview. To his credit, calcuating (40!/(r!*(40-r!))) * (.5^r) * (.5^(40-r)) for 40 values of r in his head would be a bit impossible.

But persons that think they have psyich abilities based on achiveiving results greater than chance (and those that refute them) should take a look at probability staistics. The flame-thrower challenger and posts about meta-analysis of psychic ability come to mind.

I can see someone sitting at home questioning whether they have psychic ability. They toss a penny 40 times calling heads or tails. They calculate getting it right 15 times out of 40 is 15/40 = 37.5%. But they achieve this 96% of the time! Amazing!! Or calculate that getting it right 20 times out of 40 is 20/40 = 50%. But they get it 60%. With a standard deviation of 3.2, that is more than 3 standard deviations!!! Holy Cow!!!! ;)

[TeaBag420]

Originally posted by DevilsAdvocate
I hope Randi has a bit more knowledge of statistics than what he let on in the King interview. To his credit, calcuating (40!/(r!*(40-r!))) * (.5^r) * (.5^(40-r)) for 40 values of r in his head would be a bit impossible.

Please Lord, let my strawman pass unseenth. Is that what he was being asked to calculate? The only reason I ask is that 40 - r! is a negative number for most values of r, meaning that the expression you posted usually evaluates to a negative number, which would be unusual for a probability.

Further, since the question under discussion was one of probability, Randi's knowledge of statistics would be irrelevant. Your error, and Randi's.


But persons that think they have psyich abilities based on achiveiving results greater than chance (and those that refute them) should take a look at probability staistics. The flame-thrower challenger and posts about meta-analysis of psychic ability come to mind.

I can see someone sitting at home questioning whether they have psychic ability. They toss a penny 40 times calling heads or tails. They calculate getting it right 15 times out of 40 is 15/40 = 37.5%. But they achieve this 96% of the time! Amazing!! Or calculate that getting it right 20 times out of 40 is 20/40 = 50%. But they get it 60%. With a standard deviation of 3.2, that is more than 3 standard deviations!!! Holy Cow!!!! ;)

I am not a staistician, nor do I know staistics, but I could get one to help me read your posts 15 out of 40 times.

"standard deviation"... Is there really such a thing as "3.2 standard deviations"?

[DevilsAdvocate]

Originally posted by TeaBag420


Please Lord, let my strawman pass unseenth. Is that what he was being asked to calculate? The only reason I ask is that 40 - r! is a negative number for most values of r, meaning that the expression you posted usually evaluates to a negative number, which would be unusual for a probability.

Further, since the question under discussion was one of probability, Randi's knowledge of statistics would be irrelevant. Your error, and Randi's.



I am not a staistician, nor do I know staistics, but I could get one to help me read your posts 15 out of 40 times.

"standard deviation"... Is there really such a thing as "3.2 standard deviations"? [/B] I did exclude some parentheses from the equation. More correctly it should be: 40!/(r!*(40-r!))) * (.5^r) * (.5^(40-r)).

40 - r! is never negative. r = the number of right answers, which must be 0 to 40. Therefore 40 - r must be 40 to 0. Sorry if the parantheses error messed things up.

Yes, Virginia, there is such a thing as a standard deviation, I believe the post by JamesM in this thread does a good job of showing such.

[DevilsAdvocate]

I just want to present facts, as best I know. But you did ask a couple of questions that I didn't answer:

Is that what he (I assume Randi in the King interview) was being asked to calculate?Yep. Randi would have had to calculate 40!/(r!*(40-r!))) * (.5^r) * (.5^(40-r)) for all possibilites of r for 1 to 40 t calculate the acutal possibilities of chance. Of course even if Randi had pre-calculated the results, he would not (or should not) commit to any specific number because (as I said) the questions will almost certainly not have exaclty 50% of success and the protocol for selceting the questions and the subject can change the results (on both sides).

Further, since the question under discussion was one of probability, Randi's knowledge of statistics would be irrelevant. Your error, and Randi's.True. I addressed the question of probability in one post. You also presented a post about Randi's "knowing statisticians" based on the King interview. I thought I addressed this as well in anther and that you agreed.

If I haven't covered anything here, post back and I'll address it.

Thanks for you posts! :)

[69dodge]

Originally posted by plindboe
Thanks for the help, but this seems like too low a probability to me. I mean, with a coin toss, getting 30 tails out of 40 coin tosses shouldn't be that hard, just random chance

I know most people don't have a good sense of statistics, myself included, but 30/40 just seems like nothing out of the ordinary to me.My calculations give the same low probability. Try flipping a coin 40 times and see what happens.Originally posted by JamesM
Incidentally, if you're interested in the number you'd have to get right for a certain level of significance, here they are, for 40 trials:

5%: 23/40
1%: 27/40
0.1%: 30/40I agree with DevilsAdvocate's table, according to which the numbers would be:<blockquote>5% : 26/40
1% : 28/40
0.1% : 31/40</blockquote>How did you get your numbers?Originally posted by DevilsAdvocate
I did exclude some parentheses from the equation. More correctly it should be: 40!/(r!*(40-r!))) * (.5^r) * (.5^(40-r)).

40 - r! is never negativeThat's the same as before. You meant "(40 - r)!".

[DevilsAdvocate]

Originally posted by 69dodge
That's the same as before. You meant "(40 - r)!". ARRRGG. I can never get my paranteses straight. How's this:

40!/((r!*(40-r)!)*(.5^r)*(.5^(40-r)))

I thnk I've got it. So, working backwards: r = right, t = trials, p = probabilty of success for each qeustion, t should be:

t!/((r!*(t-r)!)*(p^r)*(p^(t-r)))

Did I type it right that time? (Anyway, the numbers I posted should be correct.)

[69dodge]

Originally posted by DevilsAdvocate
ARRRGG. I can never get my paranteses straight. How's this:

40!/((r!*(40-r)!)*(.5^r)*(.5^(40-r)))

I thnk I've got it. So, working backwards: r = right, t = trials, p = probabilty of success for each qeustion, t should be:

t!/((r!*(t-r)!)*(p^r)*(p^(t-r)))

Did I type it right that time? (Anyway, the numbers I posted should be correct.)The powers don't belong in the denominator. And for general p, it's 1 - p, not p, that gets raised to t - r. (Of course, when p is 1/2, so is 1 - p.)

t! / [r! * (t - r)!] * p^r * (1 - p)^(t - r)

Yes, your numbers are correct.

[69dodge]

Originally posted by geni
The probability for gettting 50/50 is about 1/4 so don't be suppised that the probability falls off fastHow'd you get 1/4?

I get half that: 0.12537...

[DevilsAdvocate]

Originally posted by 69dodge
How'd you get 1/4?

I get half that: 0.12537... I'm not sure what the calculation is. Is it getting 50 out of 50 questions (with 50% probability each) all correct? If it is, that would be very very small. How do you get .12537?

[69dodge]

Originally posted by DevilsAdvocate
I'm not sure what the calculation is. Is it getting 50 out of 50 questions (with 50% probability each) all correct? If it is, that would be very very small. How do you get .12537?I figured he meant half right and half wrong, i.e., 20 correct out of a total of 40. (Read "50/50" as "fifty fifty", not "fifty out of fifty").

[DevilsAdvocate]

Originally posted by 69dodge
I figured he meant half right and half wrong, i.e., 20 correct out of a total of 40. (Read "50/50" as "fifty fifty", not "fifty out of fifty"). Yeah, I still don't understand. As long as we can agree that 50 out of 50 would be more than one billlion to one.

[69dodge]

Originally posted by DevilsAdvocate
As long as we can agree that 50 out of 50 would be more than one billlion to one.Yes indeed. 2⁵⁰. Which is about 10¹⁵. Which is much more than a billion. Even the British kind.

[Drooper]

What I don't really understand reading the transcript is why Randi didn't give a better repsonse to the statistical isssue that seem to become very confused.

He should have said that every outcome would be partly the result of chance and that repeated trials and the use of a proper statistical test would help identify how much of the result was chance and what was due to true psychic effect.

Then when pressed about specific tests he should have made it clear that in every instance the require hurdle would be set in such a way that there was only a 1 in (say) 10,000 chance that the result could have occured by chance (for a preliminary test) or 1 chance in one million (for a shot at the million bucks). And because everyone gets a test tailored to their own needs this will translate into somethin different for each applicant - maybe 35 hits out of 40 for a psychic, 10 hits out of 20 for a dowser etc.

As it is King seems to have have completely confused himself and probably most of his audience as well.

[JamesM]

Originally posted by 69dodge
How did you get your numbers?
By totally sucking. I did my calculations on a spreadsheet and then proceeded to read off the wrong row of numbers. Oops! How embarrassing.

[geni]

Originally posted by 69dodge
How'd you get 1/4?

I get half that: 0.12537...

By doing the maths late at night and thinking ~0.125 =1/4 rather than 1/8. i was of course wrong.

[T'ai Chi]

Originally posted by TeaBag420

If he hires people to evaluate their qualifications, who evaluates THEIR qualifications?


The M.S. and Ph.D committees of the universities in question and fellow statisticians I'd imagine.

[T'ai Chi]

Originally posted by Drooper
What I don't really understand reading the transcript is why Randi didn't give a better repsonse to the statistical isssue that seem to become very confused.


Before going to the show, he could have had a table perpared showing the total number of questions (n), and the number of those needed to pass (r), for a given number of choices (1/p) in n multiple choice questions.

Then he could just refer to this paper.

If King or Browne propose different p or n, he could just say that these numbers have to be recalculated for different n and p, something which an unbiased statistician will do if Slyvia is interested...

[T'ai Chi]

Originally posted by TeaBag420

"standard deviation"... Is there really such a thing as "3.2 standard deviations"?

Yes.

[geni]

Originally posted by jzs
The M.S. and Ph.D committees of the universities in question and fellow statisticians I'd imagine.

Not that the statistics involved are that complicated.

[T'ai Chi]

Originally posted by geni
Not that the statistics involved are that complicated.

Nope, not at all. I'd imagine that the level of statistics involved in the JREF tests doesn't go beyond the binomial distribution.

[Drooper]

Originally posted by jzs


Before going to the show, he could have had a table perpared showing the total number of questions (n), and the number of those needed to pass (r), for a given number of choices (1/p) in n multiple choice questions.

Then he could just refer to this paper.

If King or Browne propose different p or n, he could just say that these numbers have to be recalculated for different n and p, something which an unbiased statistician will do if Slyvia is interested... [/B]

Not even that technical.

Randi may not be a statstician, but he knows precisely that he might need a statistician to calculate the likelihood of a event occurring by chance. And he knows the neighbourhood of the likelihood that he is willing to accept as proof: usually around 1 in a million. That is all he needs to say in these instances. Clear and concise.

[drkitten]

Originally posted by TeaBag420

If Randi doesn't know statistics, how does he evaluate the qualifications of statisticians? Is there a certifying body with established standards? If he hires people to evaluate their qualifications, who evaluates THEIR qualifications?


I do.

More generally, I sit on a Ph.D. committee and listen to the candidate explain their understanding of the field in question, be it statistics, computer science, linguistics, philology, what have you. If the candidate isn't qualified for the degree s/he is proposing to take, I vote "no" and the candidate doesn't get the degree.

I am qualified to sit on that committee by virtue of a similar vote taken a number of years ago by my committee, all of whom in turn received their degrees by a vote of appropriate Ph.D. holders. (One of the people in my department is a direct umpteenth generation "descendant" of Sir Isaac Newton, I believe.)